After Big Sur upgrade, my late-2013 15" Macbook Pro also has very, very bad battery life (now I get about 1/3 of what I was getting before) and the laptop is HOT to the touch, even after just charging, and although my house is very, very cold. I just tried resetting the SMC but just in the time it's taken to type this post I've lost about 3-4% battery life! YIKES!

I have had Bluetooth problems with my beloved iPhone for years. I think I may have found the solution. Go to Settings, then Bluetooth, then look at the info for the paired device, and you’ll see something I never saw before, an option to define the kind of device it is; i.e., headset, speaker, etc. Once I did this my Bluetooth problems appear to have been solved. BTW if my info is stale, my apologies.